Interior Angle (Internal Angle): Definition, Examples, Chart, and Practice

What is an interior angle?

An interior angle is an angle inside a shape.

It is made where two sides of a polygon meet at a corner.

Interior angle and internal angle mean the same thing in this lesson. Both names point to an angle inside the shape.

Interior angle rule

Use the inside of the shape to decide if an angle is interior.

If the angle opens inside the polygon, it is an interior angle.

If the angle is drawn outside the shape, it is an exterior angle instead.

Interior angles in polygons

Every corner of a polygon has an interior angle.

A triangle has 3 interior angles, a quadrilateral has 4, a pentagon has 5, and a hexagon has 6.

When all sides and angles are equal, the shape is regular, so each interior angle has the same measure.

Interior angle sums

The inside angles of a triangle add to 180°.

A quadrilateral has an interior angle sum of 360°.

For a full triangle explanation, review angles in a triangle when you are ready for the 180° rule.

Worked example

Problem: A quadrilateral has four angles. Three of them are 90°, 80°, and 100°. What is the missing interior angle?

Step 1: A quadrilateral has an interior angle sum of 360°.

Step 2: Add the known angles: 90° + 80° + 100° = 270°.

Step 3: Subtract from 360°: 360° - 270° = 90°.

Answer: The missing interior angle is 90°.

Interior angle vs other angle ideas

A right angle can be an interior angle if it is inside a shape.

An altitude of a triangle is a height line, not an interior angle, even though it may start from a triangle corner.

The word interior tells you the angle location. The angle size can still be acute, right, obtuse, or another type.

Common mistakes

Do not count an outside angle as an interior angle.

Do not assume every interior angle is small. Some interior angles can be obtuse.

Do not use the triangle sum for every polygon. A triangle totals 180°, but a quadrilateral totals 360°.

Quick practice

1. A triangle has 3 interior angles.

2. A square has 4 interior angles, and each one is 90°.

3. Interior angle and internal angle can name the same inside angle.

4. If an angle is drawn outside the shape, it is not an interior angle.